Properties

Label 154.2.e.f.67.2
Level $154$
Weight $2$
Character 154.67
Analytic conductor $1.230$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 154 = 2 \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 154.e (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(1.22969619113\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{7})\)
Defining polynomial: \( x^{4} + 7x^{2} + 49 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.2
Root \(-1.32288 - 2.29129i\) of defining polynomial
Character \(\chi\) \(=\) 154.67
Dual form 154.2.e.f.23.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(1.32288 - 2.29129i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.82288 - 3.15731i) q^{5} +2.64575 q^{6} +(1.32288 + 2.29129i) q^{7} -1.00000 q^{8} +(-2.00000 - 3.46410i) q^{9} +(1.82288 - 3.15731i) q^{10} +(-0.500000 + 0.866025i) q^{11} +(1.32288 + 2.29129i) q^{12} +5.00000 q^{13} +(-1.32288 + 2.29129i) q^{14} -9.64575 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{18} +(0.177124 + 0.306788i) q^{19} +3.64575 q^{20} +7.00000 q^{21} -1.00000 q^{22} +(1.82288 + 3.15731i) q^{23} +(-1.32288 + 2.29129i) q^{24} +(-4.14575 + 7.18065i) q^{25} +(2.50000 + 4.33013i) q^{26} -2.64575 q^{27} -2.64575 q^{28} -4.29150 q^{29} +(-4.82288 - 8.35347i) q^{30} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.32288 + 2.29129i) q^{33} -6.00000 q^{34} +(4.82288 - 8.35347i) q^{35} +4.00000 q^{36} +(0.822876 + 1.42526i) q^{37} +(-0.177124 + 0.306788i) q^{38} +(6.61438 - 11.4564i) q^{39} +(1.82288 + 3.15731i) q^{40} -4.93725 q^{41} +(3.50000 + 6.06218i) q^{42} -4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-7.29150 + 12.6293i) q^{45} +(-1.82288 + 3.15731i) q^{46} +(-6.64575 - 11.5108i) q^{47} -2.64575 q^{48} +(-3.50000 + 6.06218i) q^{49} -8.29150 q^{50} +(7.93725 + 13.7477i) q^{51} +(-2.50000 + 4.33013i) q^{52} +(1.82288 - 3.15731i) q^{53} +(-1.32288 - 2.29129i) q^{54} +3.64575 q^{55} +(-1.32288 - 2.29129i) q^{56} +0.937254 q^{57} +(-2.14575 - 3.71655i) q^{58} +(0.322876 - 0.559237i) q^{59} +(4.82288 - 8.35347i) q^{60} +(-1.85425 - 3.21165i) q^{61} +4.00000 q^{62} +(5.29150 - 9.16515i) q^{63} +1.00000 q^{64} +(-9.11438 - 15.7866i) q^{65} +(-1.32288 + 2.29129i) q^{66} +(-1.96863 + 3.40976i) q^{67} +(-3.00000 - 5.19615i) q^{68} +9.64575 q^{69} +9.64575 q^{70} +9.64575 q^{71} +(2.00000 + 3.46410i) q^{72} +(-2.82288 + 4.88936i) q^{73} +(-0.822876 + 1.42526i) q^{74} +(10.9686 + 18.9982i) q^{75} -0.354249 q^{76} -2.64575 q^{77} +13.2288 q^{78} +(-1.32288 - 2.29129i) q^{79} +(-1.82288 + 3.15731i) q^{80} +(2.50000 - 4.33013i) q^{81} +(-2.46863 - 4.27579i) q^{82} +13.2915 q^{83} +(-3.50000 + 6.06218i) q^{84} +21.8745 q^{85} +(-2.00000 - 3.46410i) q^{86} +(-5.67712 + 9.83307i) q^{87} +(0.500000 - 0.866025i) q^{88} +(7.29150 + 12.6293i) q^{89} -14.5830 q^{90} +(6.61438 + 11.4564i) q^{91} -3.64575 q^{92} +(-5.29150 - 9.16515i) q^{93} +(6.64575 - 11.5108i) q^{94} +(0.645751 - 1.11847i) q^{95} +(-1.32288 - 2.29129i) q^{96} -5.70850 q^{97} -7.00000 q^{98} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 8 q^{9} + 2 q^{10} - 2 q^{11} + 20 q^{13} - 28 q^{15} - 2 q^{16} - 12 q^{17} + 8 q^{18} + 6 q^{19} + 4 q^{20} + 28 q^{21} - 4 q^{22} + 2 q^{23} - 6 q^{25} + 10 q^{26} + 4 q^{29} - 14 q^{30} + 8 q^{31} + 2 q^{32} - 24 q^{34} + 14 q^{35} + 16 q^{36} - 2 q^{37} - 6 q^{38} + 2 q^{40} + 12 q^{41} + 14 q^{42} - 16 q^{43} - 2 q^{44} - 8 q^{45} - 2 q^{46} - 16 q^{47} - 14 q^{49} - 12 q^{50} - 10 q^{52} + 2 q^{53} + 4 q^{55} - 28 q^{57} + 2 q^{58} - 4 q^{59} + 14 q^{60} - 18 q^{61} + 16 q^{62} + 4 q^{64} - 10 q^{65} + 8 q^{67} - 12 q^{68} + 28 q^{69} + 28 q^{70} + 28 q^{71} + 8 q^{72} - 6 q^{73} + 2 q^{74} + 28 q^{75} - 12 q^{76} - 2 q^{80} + 10 q^{81} + 6 q^{82} + 32 q^{83} - 14 q^{84} + 24 q^{85} - 8 q^{86} - 28 q^{87} + 2 q^{88} + 8 q^{89} - 16 q^{90} - 4 q^{92} + 16 q^{94} - 8 q^{95} - 44 q^{97} - 28 q^{98} + 16 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/154\mathbb{Z}\right)^\times\).

\(n\) \(45\) \(57\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) 1.32288 2.29129i 0.763763 1.32288i −0.177136 0.984186i \(-0.556683\pi\)
0.940898 0.338689i \(-0.109984\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −1.82288 3.15731i −0.815215 1.41199i −0.909174 0.416417i \(-0.863286\pi\)
0.0939588 0.995576i \(-0.470048\pi\)
\(6\) 2.64575 1.08012
\(7\) 1.32288 + 2.29129i 0.500000 + 0.866025i
\(8\) −1.00000 −0.353553
\(9\) −2.00000 3.46410i −0.666667 1.15470i
\(10\) 1.82288 3.15731i 0.576444 0.998430i
\(11\) −0.500000 + 0.866025i −0.150756 + 0.261116i
\(12\) 1.32288 + 2.29129i 0.381881 + 0.661438i
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) −1.32288 + 2.29129i −0.353553 + 0.612372i
\(15\) −9.64575 −2.49052
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 2.00000 3.46410i 0.471405 0.816497i
\(19\) 0.177124 + 0.306788i 0.0406351 + 0.0703821i 0.885628 0.464396i \(-0.153729\pi\)
−0.844993 + 0.534778i \(0.820395\pi\)
\(20\) 3.64575 0.815215
\(21\) 7.00000 1.52753
\(22\) −1.00000 −0.213201
\(23\) 1.82288 + 3.15731i 0.380096 + 0.658345i 0.991076 0.133301i \(-0.0425577\pi\)
−0.610980 + 0.791646i \(0.709224\pi\)
\(24\) −1.32288 + 2.29129i −0.270031 + 0.467707i
\(25\) −4.14575 + 7.18065i −0.829150 + 1.43613i
\(26\) 2.50000 + 4.33013i 0.490290 + 0.849208i
\(27\) −2.64575 −0.509175
\(28\) −2.64575 −0.500000
\(29\) −4.29150 −0.796912 −0.398456 0.917187i \(-0.630454\pi\)
−0.398456 + 0.917187i \(0.630454\pi\)
\(30\) −4.82288 8.35347i −0.880533 1.52513i
\(31\) 2.00000 3.46410i 0.359211 0.622171i −0.628619 0.777714i \(-0.716379\pi\)
0.987829 + 0.155543i \(0.0497126\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.32288 + 2.29129i 0.230283 + 0.398862i
\(34\) −6.00000 −1.02899
\(35\) 4.82288 8.35347i 0.815215 1.41199i
\(36\) 4.00000 0.666667
\(37\) 0.822876 + 1.42526i 0.135280 + 0.234312i 0.925704 0.378248i \(-0.123473\pi\)
−0.790424 + 0.612560i \(0.790140\pi\)
\(38\) −0.177124 + 0.306788i −0.0287334 + 0.0497676i
\(39\) 6.61438 11.4564i 1.05915 1.83450i
\(40\) 1.82288 + 3.15731i 0.288222 + 0.499215i
\(41\) −4.93725 −0.771070 −0.385535 0.922693i \(-0.625983\pi\)
−0.385535 + 0.922693i \(0.625983\pi\)
\(42\) 3.50000 + 6.06218i 0.540062 + 0.935414i
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −0.500000 0.866025i −0.0753778 0.130558i
\(45\) −7.29150 + 12.6293i −1.08695 + 1.88266i
\(46\) −1.82288 + 3.15731i −0.268768 + 0.465520i
\(47\) −6.64575 11.5108i −0.969382 1.67902i −0.697349 0.716732i \(-0.745637\pi\)
−0.272034 0.962288i \(-0.587696\pi\)
\(48\) −2.64575 −0.381881
\(49\) −3.50000 + 6.06218i −0.500000 + 0.866025i
\(50\) −8.29150 −1.17260
\(51\) 7.93725 + 13.7477i 1.11144 + 1.92507i
\(52\) −2.50000 + 4.33013i −0.346688 + 0.600481i
\(53\) 1.82288 3.15731i 0.250391 0.433690i −0.713242 0.700918i \(-0.752774\pi\)
0.963634 + 0.267227i \(0.0861074\pi\)
\(54\) −1.32288 2.29129i −0.180021 0.311805i
\(55\) 3.64575 0.491593
\(56\) −1.32288 2.29129i −0.176777 0.306186i
\(57\) 0.937254 0.124142
\(58\) −2.14575 3.71655i −0.281751 0.488007i
\(59\) 0.322876 0.559237i 0.0420348 0.0728065i −0.844243 0.535961i \(-0.819949\pi\)
0.886277 + 0.463155i \(0.153283\pi\)
\(60\) 4.82288 8.35347i 0.622631 1.07843i
\(61\) −1.85425 3.21165i −0.237412 0.411210i 0.722559 0.691310i \(-0.242966\pi\)
−0.959971 + 0.280099i \(0.909633\pi\)
\(62\) 4.00000 0.508001
\(63\) 5.29150 9.16515i 0.666667 1.15470i
\(64\) 1.00000 0.125000
\(65\) −9.11438 15.7866i −1.13050 1.95808i
\(66\) −1.32288 + 2.29129i −0.162835 + 0.282038i
\(67\) −1.96863 + 3.40976i −0.240506 + 0.416569i −0.960859 0.277039i \(-0.910647\pi\)
0.720352 + 0.693608i \(0.243980\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 9.64575 1.16121
\(70\) 9.64575 1.15289
\(71\) 9.64575 1.14474 0.572370 0.819995i \(-0.306024\pi\)
0.572370 + 0.819995i \(0.306024\pi\)
\(72\) 2.00000 + 3.46410i 0.235702 + 0.408248i
\(73\) −2.82288 + 4.88936i −0.330393 + 0.572257i −0.982589 0.185793i \(-0.940514\pi\)
0.652196 + 0.758050i \(0.273848\pi\)
\(74\) −0.822876 + 1.42526i −0.0956574 + 0.165683i
\(75\) 10.9686 + 18.9982i 1.26655 + 2.19373i
\(76\) −0.354249 −0.0406351
\(77\) −2.64575 −0.301511
\(78\) 13.2288 1.49786
\(79\) −1.32288 2.29129i −0.148835 0.257790i 0.781962 0.623326i \(-0.214219\pi\)
−0.930797 + 0.365536i \(0.880886\pi\)
\(80\) −1.82288 + 3.15731i −0.203804 + 0.352998i
\(81\) 2.50000 4.33013i 0.277778 0.481125i
\(82\) −2.46863 4.27579i −0.272614 0.472182i
\(83\) 13.2915 1.45893 0.729466 0.684017i \(-0.239769\pi\)
0.729466 + 0.684017i \(0.239769\pi\)
\(84\) −3.50000 + 6.06218i −0.381881 + 0.661438i
\(85\) 21.8745 2.37262
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) −5.67712 + 9.83307i −0.608652 + 1.05422i
\(88\) 0.500000 0.866025i 0.0533002 0.0923186i
\(89\) 7.29150 + 12.6293i 0.772898 + 1.33870i 0.935968 + 0.352084i \(0.114527\pi\)
−0.163071 + 0.986614i \(0.552140\pi\)
\(90\) −14.5830 −1.53718
\(91\) 6.61438 + 11.4564i 0.693375 + 1.20096i
\(92\) −3.64575 −0.380096
\(93\) −5.29150 9.16515i −0.548703 0.950382i
\(94\) 6.64575 11.5108i 0.685457 1.18725i
\(95\) 0.645751 1.11847i 0.0662527 0.114753i
\(96\) −1.32288 2.29129i −0.135015 0.233854i
\(97\) −5.70850 −0.579610 −0.289805 0.957086i \(-0.593590\pi\)
−0.289805 + 0.957086i \(0.593590\pi\)
\(98\) −7.00000 −0.707107
\(99\) 4.00000 0.402015
\(100\) −4.14575 7.18065i −0.414575 0.718065i
\(101\) −1.50000 + 2.59808i −0.149256 + 0.258518i −0.930953 0.365140i \(-0.881021\pi\)
0.781697 + 0.623658i \(0.214354\pi\)
\(102\) −7.93725 + 13.7477i −0.785905 + 1.36123i
\(103\) −6.46863 11.2040i −0.637373 1.10396i −0.986007 0.166703i \(-0.946688\pi\)
0.348634 0.937259i \(-0.386646\pi\)
\(104\) −5.00000 −0.490290
\(105\) −12.7601 22.1012i −1.24526 2.15686i
\(106\) 3.64575 0.354107
\(107\) −2.46863 4.27579i −0.238651 0.413356i 0.721676 0.692231i \(-0.243372\pi\)
−0.960327 + 0.278875i \(0.910039\pi\)
\(108\) 1.32288 2.29129i 0.127294 0.220479i
\(109\) −5.29150 + 9.16515i −0.506834 + 0.877862i 0.493135 + 0.869953i \(0.335851\pi\)
−0.999969 + 0.00790932i \(0.997482\pi\)
\(110\) 1.82288 + 3.15731i 0.173804 + 0.301038i
\(111\) 4.35425 0.413287
\(112\) 1.32288 2.29129i 0.125000 0.216506i
\(113\) −7.70850 −0.725154 −0.362577 0.931954i \(-0.618103\pi\)
−0.362577 + 0.931954i \(0.618103\pi\)
\(114\) 0.468627 + 0.811686i 0.0438909 + 0.0760213i
\(115\) 6.64575 11.5108i 0.619720 1.07339i
\(116\) 2.14575 3.71655i 0.199228 0.345073i
\(117\) −10.0000 17.3205i −0.924500 1.60128i
\(118\) 0.645751 0.0594462
\(119\) −15.8745 −1.45521
\(120\) 9.64575 0.880533
\(121\) −0.500000 0.866025i −0.0454545 0.0787296i
\(122\) 1.85425 3.21165i 0.167876 0.290769i
\(123\) −6.53137 + 11.3127i −0.588914 + 1.02003i
\(124\) 2.00000 + 3.46410i 0.179605 + 0.311086i
\(125\) 12.0000 1.07331
\(126\) 10.5830 0.942809
\(127\) 0.0627461 0.00556781 0.00278391 0.999996i \(-0.499114\pi\)
0.00278391 + 0.999996i \(0.499114\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −5.29150 + 9.16515i −0.465891 + 0.806947i
\(130\) 9.11438 15.7866i 0.799384 1.38457i
\(131\) −7.82288 13.5496i −0.683488 1.18384i −0.973909 0.226937i \(-0.927129\pi\)
0.290422 0.956899i \(-0.406204\pi\)
\(132\) −2.64575 −0.230283
\(133\) −0.468627 + 0.811686i −0.0406351 + 0.0703821i
\(134\) −3.93725 −0.340127
\(135\) 4.82288 + 8.35347i 0.415087 + 0.718952i
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −9.43725 + 16.3458i −0.806279 + 1.39652i 0.109145 + 0.994026i \(0.465189\pi\)
−0.915424 + 0.402490i \(0.868145\pi\)
\(138\) 4.82288 + 8.35347i 0.410550 + 0.711094i
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 4.82288 + 8.35347i 0.407607 + 0.705997i
\(141\) −35.1660 −2.96151
\(142\) 4.82288 + 8.35347i 0.404727 + 0.701007i
\(143\) −2.50000 + 4.33013i −0.209061 + 0.362103i
\(144\) −2.00000 + 3.46410i −0.166667 + 0.288675i
\(145\) 7.82288 + 13.5496i 0.649654 + 1.12523i
\(146\) −5.64575 −0.467246
\(147\) 9.26013 + 16.0390i 0.763763 + 1.32288i
\(148\) −1.64575 −0.135280
\(149\) 2.35425 + 4.07768i 0.192868 + 0.334056i 0.946199 0.323584i \(-0.104888\pi\)
−0.753332 + 0.657641i \(0.771555\pi\)
\(150\) −10.9686 + 18.9982i −0.895585 + 1.55120i
\(151\) 1.67712 2.90486i 0.136482 0.236395i −0.789680 0.613519i \(-0.789754\pi\)
0.926163 + 0.377124i \(0.123087\pi\)
\(152\) −0.177124 0.306788i −0.0143667 0.0248838i
\(153\) 24.0000 1.94029
\(154\) −1.32288 2.29129i −0.106600 0.184637i
\(155\) −14.5830 −1.17134
\(156\) 6.61438 + 11.4564i 0.529574 + 0.917249i
\(157\) 10.5830 18.3303i 0.844616 1.46292i −0.0413387 0.999145i \(-0.513162\pi\)
0.885954 0.463772i \(-0.153504\pi\)
\(158\) 1.32288 2.29129i 0.105242 0.182285i
\(159\) −4.82288 8.35347i −0.382479 0.662473i
\(160\) −3.64575 −0.288222
\(161\) −4.82288 + 8.35347i −0.380096 + 0.658345i
\(162\) 5.00000 0.392837
\(163\) 2.32288 + 4.02334i 0.181942 + 0.315132i 0.942542 0.334089i \(-0.108428\pi\)
−0.760600 + 0.649221i \(0.775095\pi\)
\(164\) 2.46863 4.27579i 0.192767 0.333883i
\(165\) 4.82288 8.35347i 0.375460 0.650316i
\(166\) 6.64575 + 11.5108i 0.515810 + 0.893410i
\(167\) 15.2288 1.17844 0.589218 0.807974i \(-0.299436\pi\)
0.589218 + 0.807974i \(0.299436\pi\)
\(168\) −7.00000 −0.540062
\(169\) 12.0000 0.923077
\(170\) 10.9373 + 18.9439i 0.838849 + 1.45293i
\(171\) 0.708497 1.22715i 0.0541801 0.0938428i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) −5.14575 8.91270i −0.391224 0.677620i 0.601387 0.798958i \(-0.294615\pi\)
−0.992611 + 0.121338i \(0.961282\pi\)
\(174\) −11.3542 −0.860763
\(175\) −21.9373 −1.65830
\(176\) 1.00000 0.0753778
\(177\) −0.854249 1.47960i −0.0642093 0.111214i
\(178\) −7.29150 + 12.6293i −0.546521 + 0.946603i
\(179\) 2.03137 3.51844i 0.151832 0.262981i −0.780069 0.625693i \(-0.784816\pi\)
0.931901 + 0.362713i \(0.118149\pi\)
\(180\) −7.29150 12.6293i −0.543477 0.941329i
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −6.61438 + 11.4564i −0.490290 + 0.849208i
\(183\) −9.81176 −0.725306
\(184\) −1.82288 3.15731i −0.134384 0.232760i
\(185\) 3.00000 5.19615i 0.220564 0.382029i
\(186\) 5.29150 9.16515i 0.387992 0.672022i
\(187\) −3.00000 5.19615i −0.219382 0.379980i
\(188\) 13.2915 0.969382
\(189\) −3.50000 6.06218i −0.254588 0.440959i
\(190\) 1.29150 0.0936954
\(191\) 6.64575 + 11.5108i 0.480870 + 0.832891i 0.999759 0.0219507i \(-0.00698768\pi\)
−0.518889 + 0.854841i \(0.673654\pi\)
\(192\) 1.32288 2.29129i 0.0954703 0.165359i
\(193\) 5.76013 9.97684i 0.414623 0.718148i −0.580766 0.814071i \(-0.697247\pi\)
0.995389 + 0.0959224i \(0.0305801\pi\)
\(194\) −2.85425 4.94370i −0.204923 0.354937i
\(195\) −48.2288 −3.45373
\(196\) −3.50000 6.06218i −0.250000 0.433013i
\(197\) 18.8745 1.34475 0.672377 0.740209i \(-0.265274\pi\)
0.672377 + 0.740209i \(0.265274\pi\)
\(198\) 2.00000 + 3.46410i 0.142134 + 0.246183i
\(199\) 11.1144 19.2507i 0.787877 1.36464i −0.139388 0.990238i \(-0.544513\pi\)
0.927265 0.374406i \(-0.122153\pi\)
\(200\) 4.14575 7.18065i 0.293149 0.507749i
\(201\) 5.20850 + 9.02138i 0.367379 + 0.636319i
\(202\) −3.00000 −0.211079
\(203\) −5.67712 9.83307i −0.398456 0.690146i
\(204\) −15.8745 −1.11144
\(205\) 9.00000 + 15.5885i 0.628587 + 1.08875i
\(206\) 6.46863 11.2040i 0.450691 0.780619i
\(207\) 7.29150 12.6293i 0.506794 0.877794i
\(208\) −2.50000 4.33013i −0.173344 0.300240i
\(209\) −0.354249 −0.0245039
\(210\) 12.7601 22.1012i 0.880533 1.52513i
\(211\) −14.9373 −1.02832 −0.514161 0.857693i \(-0.671897\pi\)
−0.514161 + 0.857693i \(0.671897\pi\)
\(212\) 1.82288 + 3.15731i 0.125196 + 0.216845i
\(213\) 12.7601 22.1012i 0.874310 1.51435i
\(214\) 2.46863 4.27579i 0.168752 0.292287i
\(215\) 7.29150 + 12.6293i 0.497276 + 0.861308i
\(216\) 2.64575 0.180021
\(217\) 10.5830 0.718421
\(218\) −10.5830 −0.716772
\(219\) 7.46863 + 12.9360i 0.504683 + 0.874137i
\(220\) −1.82288 + 3.15731i −0.122898 + 0.212866i
\(221\) −15.0000 + 25.9808i −1.00901 + 1.74766i
\(222\) 2.17712 + 3.77089i 0.146119 + 0.253086i
\(223\) −12.3542 −0.827302 −0.413651 0.910436i \(-0.635747\pi\)
−0.413651 + 0.910436i \(0.635747\pi\)
\(224\) 2.64575 0.176777
\(225\) 33.1660 2.21107
\(226\) −3.85425 6.67575i −0.256381 0.444065i
\(227\) 6.64575 11.5108i 0.441094 0.763997i −0.556677 0.830729i \(-0.687924\pi\)
0.997771 + 0.0667318i \(0.0212572\pi\)
\(228\) −0.468627 + 0.811686i −0.0310356 + 0.0537552i
\(229\) 8.00000 + 13.8564i 0.528655 + 0.915657i 0.999442 + 0.0334101i \(0.0106368\pi\)
−0.470787 + 0.882247i \(0.656030\pi\)
\(230\) 13.2915 0.876416
\(231\) −3.50000 + 6.06218i −0.230283 + 0.398862i
\(232\) 4.29150 0.281751
\(233\) −8.46863 14.6681i −0.554798 0.960939i −0.997919 0.0644769i \(-0.979462\pi\)
0.443121 0.896462i \(-0.353871\pi\)
\(234\) 10.0000 17.3205i 0.653720 1.13228i
\(235\) −24.2288 + 41.9654i −1.58051 + 2.73752i
\(236\) 0.322876 + 0.559237i 0.0210174 + 0.0364032i
\(237\) −7.00000 −0.454699
\(238\) −7.93725 13.7477i −0.514496 0.891133i
\(239\) 9.22876 0.596959 0.298479 0.954416i \(-0.403521\pi\)
0.298479 + 0.954416i \(0.403521\pi\)
\(240\) 4.82288 + 8.35347i 0.311315 + 0.539214i
\(241\) −11.4059 + 19.7556i −0.734717 + 1.27257i 0.220130 + 0.975471i \(0.429352\pi\)
−0.954847 + 0.297097i \(0.903981\pi\)
\(242\) 0.500000 0.866025i 0.0321412 0.0556702i
\(243\) −10.5830 18.3303i −0.678900 1.17589i
\(244\) 3.70850 0.237412
\(245\) 25.5203 1.63043
\(246\) −13.0627 −0.832850
\(247\) 0.885622 + 1.53394i 0.0563508 + 0.0976024i
\(248\) −2.00000 + 3.46410i −0.127000 + 0.219971i
\(249\) 17.5830 30.4547i 1.11428 1.92999i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) 7.29150 0.460236 0.230118 0.973163i \(-0.426089\pi\)
0.230118 + 0.973163i \(0.426089\pi\)
\(252\) 5.29150 + 9.16515i 0.333333 + 0.577350i
\(253\) −3.64575 −0.229206
\(254\) 0.0313730 + 0.0543397i 0.00196852 + 0.00340958i
\(255\) 28.9373 50.1208i 1.81212 3.13869i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0.208497 + 0.361128i 0.0130057 + 0.0225265i 0.872455 0.488694i \(-0.162527\pi\)
−0.859449 + 0.511221i \(0.829193\pi\)
\(258\) −10.5830 −0.658869
\(259\) −2.17712 + 3.77089i −0.135280 + 0.234312i
\(260\) 18.2288 1.13050
\(261\) 8.58301 + 14.8662i 0.531275 + 0.920195i
\(262\) 7.82288 13.5496i 0.483299 0.837098i
\(263\) −2.03137 + 3.51844i −0.125260 + 0.216956i −0.921834 0.387584i \(-0.873310\pi\)
0.796575 + 0.604540i \(0.206643\pi\)
\(264\) −1.32288 2.29129i −0.0814174 0.141019i
\(265\) −13.2915 −0.816491
\(266\) −0.937254 −0.0574667
\(267\) 38.5830 2.36124
\(268\) −1.96863 3.40976i −0.120253 0.208284i
\(269\) −13.2915 + 23.0216i −0.810397 + 1.40365i 0.102189 + 0.994765i \(0.467415\pi\)
−0.912586 + 0.408884i \(0.865918\pi\)
\(270\) −4.82288 + 8.35347i −0.293511 + 0.508376i
\(271\) 8.96863 + 15.5341i 0.544805 + 0.943630i 0.998619 + 0.0525339i \(0.0167298\pi\)
−0.453814 + 0.891097i \(0.649937\pi\)
\(272\) 6.00000 0.363803
\(273\) 35.0000 2.11830
\(274\) −18.8745 −1.14025
\(275\) −4.14575 7.18065i −0.249998 0.433010i
\(276\) −4.82288 + 8.35347i −0.290303 + 0.502820i
\(277\) 5.85425 10.1399i 0.351748 0.609245i −0.634808 0.772670i \(-0.718921\pi\)
0.986556 + 0.163425i \(0.0522542\pi\)
\(278\) −2.00000 3.46410i −0.119952 0.207763i
\(279\) −16.0000 −0.957895
\(280\) −4.82288 + 8.35347i −0.288222 + 0.499215i
\(281\) −7.06275 −0.421328 −0.210664 0.977559i \(-0.567563\pi\)
−0.210664 + 0.977559i \(0.567563\pi\)
\(282\) −17.5830 30.4547i −1.04705 1.81355i
\(283\) 3.82288 6.62141i 0.227246 0.393602i −0.729745 0.683720i \(-0.760361\pi\)
0.956991 + 0.290118i \(0.0936944\pi\)
\(284\) −4.82288 + 8.35347i −0.286185 + 0.495687i
\(285\) −1.70850 2.95920i −0.101203 0.175288i
\(286\) −5.00000 −0.295656
\(287\) −6.53137 11.3127i −0.385535 0.667766i
\(288\) −4.00000 −0.235702
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −7.82288 + 13.5496i −0.459375 + 0.795661i
\(291\) −7.55163 + 13.0798i −0.442685 + 0.766752i
\(292\) −2.82288 4.88936i −0.165196 0.286128i
\(293\) 12.0000 0.701047 0.350524 0.936554i \(-0.386004\pi\)
0.350524 + 0.936554i \(0.386004\pi\)
\(294\) −9.26013 + 16.0390i −0.540062 + 0.935414i
\(295\) −2.35425 −0.137070
\(296\) −0.822876 1.42526i −0.0478287 0.0828417i
\(297\) 1.32288 2.29129i 0.0767610 0.132954i
\(298\) −2.35425 + 4.07768i −0.136378 + 0.236214i
\(299\) 9.11438 + 15.7866i 0.527098 + 0.912961i
\(300\) −21.9373 −1.26655
\(301\) −5.29150 9.16515i −0.304997 0.528271i
\(302\) 3.35425 0.193015
\(303\) 3.96863 + 6.87386i 0.227992 + 0.394893i
\(304\) 0.177124 0.306788i 0.0101588 0.0175955i
\(305\) −6.76013 + 11.7089i −0.387084 + 0.670449i
\(306\) 12.0000 + 20.7846i 0.685994 + 1.18818i
\(307\) −4.22876 −0.241348 −0.120674 0.992692i \(-0.538506\pi\)
−0.120674 + 0.992692i \(0.538506\pi\)
\(308\) 1.32288 2.29129i 0.0753778 0.130558i
\(309\) −34.2288 −1.94721
\(310\) −7.29150 12.6293i −0.414130 0.717293i
\(311\) −8.46863 + 14.6681i −0.480212 + 0.831751i −0.999742 0.0227007i \(-0.992774\pi\)
0.519531 + 0.854452i \(0.326107\pi\)
\(312\) −6.61438 + 11.4564i −0.374465 + 0.648593i
\(313\) −1.20850 2.09318i −0.0683083 0.118313i 0.829848 0.557989i \(-0.188427\pi\)
−0.898157 + 0.439675i \(0.855093\pi\)
\(314\) 21.1660 1.19447
\(315\) −38.5830 −2.17391
\(316\) 2.64575 0.148835
\(317\) −6.00000 10.3923i −0.336994 0.583690i 0.646872 0.762598i \(-0.276077\pi\)
−0.983866 + 0.178908i \(0.942743\pi\)
\(318\) 4.82288 8.35347i 0.270453 0.468439i
\(319\) 2.14575 3.71655i 0.120139 0.208087i
\(320\) −1.82288 3.15731i −0.101902 0.176499i
\(321\) −13.0627 −0.729091
\(322\) −9.64575 −0.537537
\(323\) −2.12549 −0.118266
\(324\) 2.50000 + 4.33013i 0.138889 + 0.240563i
\(325\) −20.7288 + 35.9033i −1.14982 + 1.99155i
\(326\) −2.32288 + 4.02334i −0.128652 + 0.222832i
\(327\) 14.0000 + 24.2487i 0.774202 + 1.34096i
\(328\) 4.93725 0.272614
\(329\) 17.5830 30.4547i 0.969382 1.67902i
\(330\) 9.64575 0.530981
\(331\) 7.67712 + 13.2972i 0.421973 + 0.730879i 0.996132 0.0878650i \(-0.0280044\pi\)
−0.574159 + 0.818743i \(0.694671\pi\)
\(332\) −6.64575 + 11.5108i −0.364733 + 0.631736i
\(333\) 3.29150 5.70105i 0.180373 0.312416i
\(334\) 7.61438 + 13.1885i 0.416640 + 0.721642i
\(335\) 14.3542 0.784256
\(336\) −3.50000 6.06218i −0.190941 0.330719i
\(337\) 24.9373 1.35842 0.679209 0.733945i \(-0.262323\pi\)
0.679209 + 0.733945i \(0.262323\pi\)
\(338\) 6.00000 + 10.3923i 0.326357 + 0.565267i
\(339\) −10.1974 + 17.6624i −0.553846 + 0.959289i
\(340\) −10.9373 + 18.9439i −0.593156 + 1.02738i
\(341\) 2.00000 + 3.46410i 0.108306 + 0.187592i
\(342\) 1.41699 0.0766223
\(343\) −18.5203 −1.00000
\(344\) 4.00000 0.215666
\(345\) −17.5830 30.4547i −0.946637 1.63962i
\(346\) 5.14575 8.91270i 0.276637 0.479150i
\(347\) −13.4059 + 23.2197i −0.719665 + 1.24650i 0.241467 + 0.970409i \(0.422371\pi\)
−0.961132 + 0.276088i \(0.910962\pi\)
\(348\) −5.67712 9.83307i −0.304326 0.527108i
\(349\) 29.8745 1.59915 0.799573 0.600569i \(-0.205059\pi\)
0.799573 + 0.600569i \(0.205059\pi\)
\(350\) −10.9686 18.9982i −0.586298 1.01550i
\(351\) −13.2288 −0.706099
\(352\) 0.500000 + 0.866025i 0.0266501 + 0.0461593i
\(353\) 17.5830 30.4547i 0.935849 1.62094i 0.162736 0.986670i \(-0.447968\pi\)
0.773113 0.634268i \(-0.218699\pi\)
\(354\) 0.854249 1.47960i 0.0454028 0.0786400i
\(355\) −17.5830 30.4547i −0.933209 1.61637i
\(356\) −14.5830 −0.772898
\(357\) −21.0000 + 36.3731i −1.11144 + 1.92507i
\(358\) 4.06275 0.214723
\(359\) 5.03137 + 8.71459i 0.265546 + 0.459939i 0.967706 0.252080i \(-0.0811145\pi\)
−0.702161 + 0.712018i \(0.747781\pi\)
\(360\) 7.29150 12.6293i 0.384296 0.665620i
\(361\) 9.43725 16.3458i 0.496698 0.860305i
\(362\) −5.00000 8.66025i −0.262794 0.455173i
\(363\) −2.64575 −0.138866
\(364\) −13.2288 −0.693375
\(365\) 20.5830 1.07736
\(366\) −4.90588 8.49723i −0.256435 0.444158i
\(367\) 4.88562 8.46215i 0.255027 0.441720i −0.709876 0.704327i \(-0.751249\pi\)
0.964903 + 0.262607i \(0.0845822\pi\)
\(368\) 1.82288 3.15731i 0.0950240 0.164586i
\(369\) 9.87451 + 17.1031i 0.514046 + 0.890354i
\(370\) 6.00000 0.311925
\(371\) 9.64575 0.500782
\(372\) 10.5830 0.548703
\(373\) 5.43725 + 9.41760i 0.281530 + 0.487625i 0.971762 0.235964i \(-0.0758247\pi\)
−0.690232 + 0.723589i \(0.742491\pi\)
\(374\) 3.00000 5.19615i 0.155126 0.268687i
\(375\) 15.8745 27.4955i 0.819756 1.41986i
\(376\) 6.64575 + 11.5108i 0.342728 + 0.593623i
\(377\) −21.4575 −1.10512
\(378\) 3.50000 6.06218i 0.180021 0.311805i
\(379\) 21.9373 1.12684 0.563421 0.826170i \(-0.309485\pi\)
0.563421 + 0.826170i \(0.309485\pi\)
\(380\) 0.645751 + 1.11847i 0.0331263 + 0.0573765i
\(381\) 0.0830052 0.143769i 0.00425249 0.00736552i
\(382\) −6.64575 + 11.5108i −0.340026 + 0.588943i
\(383\) 17.0516 + 29.5343i 0.871298 + 1.50913i 0.860655 + 0.509189i \(0.170054\pi\)
0.0106427 + 0.999943i \(0.496612\pi\)
\(384\) 2.64575 0.135015
\(385\) 4.82288 + 8.35347i 0.245797 + 0.425732i
\(386\) 11.5203 0.586366
\(387\) 8.00000 + 13.8564i 0.406663 + 0.704361i
\(388\) 2.85425 4.94370i 0.144903 0.250979i
\(389\) 10.4059 18.0235i 0.527599 0.913828i −0.471883 0.881661i \(-0.656426\pi\)
0.999482 0.0321675i \(-0.0102410\pi\)
\(390\) −24.1144 41.7673i −1.22108 2.11497i
\(391\) −21.8745 −1.10624
\(392\) 3.50000 6.06218i 0.176777 0.306186i
\(393\) −41.3948 −2.08809
\(394\) 9.43725 + 16.3458i 0.475442 + 0.823490i
\(395\) −4.82288 + 8.35347i −0.242665 + 0.420308i
\(396\) −2.00000 + 3.46410i −0.100504 + 0.174078i
\(397\) −15.5830 26.9906i −0.782089 1.35462i −0.930723 0.365725i \(-0.880821\pi\)
0.148634 0.988892i \(-0.452512\pi\)
\(398\) 22.2288 1.11423
\(399\) 1.23987 + 2.14752i 0.0620712 + 0.107510i
\(400\) 8.29150 0.414575
\(401\) −0.208497 0.361128i −0.0104119 0.0180339i 0.860773 0.508990i \(-0.169981\pi\)
−0.871184 + 0.490956i \(0.836648\pi\)
\(402\) −5.20850 + 9.02138i −0.259776 + 0.449946i
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) −1.50000 2.59808i −0.0746278 0.129259i
\(405\) −18.2288 −0.905794
\(406\) 5.67712 9.83307i 0.281751 0.488007i
\(407\) −1.64575 −0.0815769
\(408\) −7.93725 13.7477i −0.392953 0.680614i
\(409\) −9.46863 + 16.4001i −0.468193 + 0.810935i −0.999339 0.0363456i \(-0.988428\pi\)
0.531146 + 0.847280i \(0.321762\pi\)
\(410\) −9.00000 + 15.5885i −0.444478 + 0.769859i
\(411\) 24.9686 + 43.2469i 1.23161 + 2.13321i
\(412\) 12.9373 0.637373
\(413\) 1.70850 0.0840697
\(414\) 14.5830 0.716716
\(415\) −24.2288 41.9654i −1.18934 2.06000i
\(416\) 2.50000 4.33013i 0.122573 0.212302i
\(417\) −5.29150 + 9.16515i −0.259126 + 0.448819i
\(418\) −0.177124 0.306788i −0.00866343 0.0150055i
\(419\) 21.8745 1.06864 0.534320 0.845282i \(-0.320568\pi\)
0.534320 + 0.845282i \(0.320568\pi\)
\(420\) 25.5203 1.24526
\(421\) −33.1660 −1.61641 −0.808206 0.588900i \(-0.799561\pi\)
−0.808206 + 0.588900i \(0.799561\pi\)
\(422\) −7.46863 12.9360i −0.363567 0.629717i
\(423\) −26.5830 + 46.0431i −1.29251 + 2.23869i
\(424\) −1.82288 + 3.15731i −0.0885267 + 0.153333i
\(425\) −24.8745 43.0839i −1.20659 2.08988i
\(426\) 25.5203 1.23646
\(427\) 4.90588 8.49723i 0.237412 0.411210i
\(428\) 4.93725 0.238651
\(429\) 6.61438 + 11.4564i 0.319345 + 0.553122i
\(430\) −7.29150 + 12.6293i −0.351627 + 0.609037i
\(431\) −1.38562 + 2.39997i −0.0667430 + 0.115602i −0.897466 0.441084i \(-0.854594\pi\)
0.830723 + 0.556686i \(0.187927\pi\)
\(432\) 1.32288 + 2.29129i 0.0636469 + 0.110240i
\(433\) −16.0000 −0.768911 −0.384455 0.923144i \(-0.625611\pi\)
−0.384455 + 0.923144i \(0.625611\pi\)
\(434\) 5.29150 + 9.16515i 0.254000 + 0.439941i
\(435\) 41.3948 1.98473
\(436\) −5.29150 9.16515i −0.253417 0.438931i
\(437\) −0.645751 + 1.11847i −0.0308905 + 0.0535039i
\(438\) −7.46863 + 12.9360i −0.356865 + 0.618108i
\(439\) 5.96863 + 10.3380i 0.284867 + 0.493404i 0.972577 0.232581i \(-0.0747172\pi\)
−0.687710 + 0.725986i \(0.741384\pi\)
\(440\) −3.64575 −0.173804
\(441\) 28.0000 1.33333
\(442\) −30.0000 −1.42695
\(443\) 9.22876 + 15.9847i 0.438471 + 0.759455i 0.997572 0.0696451i \(-0.0221867\pi\)
−0.559100 + 0.829100i \(0.688853\pi\)
\(444\) −2.17712 + 3.77089i −0.103322 + 0.178959i
\(445\) 26.5830 46.0431i 1.26016 2.18265i
\(446\) −6.17712 10.6991i −0.292495 0.506617i
\(447\) 12.4575 0.589220
\(448\) 1.32288 + 2.29129i 0.0625000 + 0.108253i
\(449\) 9.87451 0.466007 0.233003 0.972476i \(-0.425145\pi\)
0.233003 + 0.972476i \(0.425145\pi\)
\(450\) 16.5830 + 28.7226i 0.781730 + 1.35400i
\(451\) 2.46863 4.27579i 0.116243 0.201339i
\(452\) 3.85425 6.67575i 0.181289 0.314001i
\(453\) −4.43725 7.68555i −0.208480 0.361099i
\(454\) 13.2915 0.623801
\(455\) 24.1144 41.7673i 1.13050 1.95808i
\(456\) −0.937254 −0.0438909
\(457\) 19.5830 + 33.9188i 0.916054 + 1.58665i 0.805350 + 0.592799i \(0.201977\pi\)
0.110704 + 0.993853i \(0.464689\pi\)
\(458\) −8.00000 + 13.8564i −0.373815 + 0.647467i
\(459\) 7.93725 13.7477i 0.370479 0.641689i
\(460\) 6.64575 + 11.5108i 0.309860 + 0.536693i
\(461\) −32.1660 −1.49812 −0.749060 0.662502i \(-0.769495\pi\)
−0.749060 + 0.662502i \(0.769495\pi\)
\(462\) −7.00000 −0.325669
\(463\) −22.4575 −1.04369 −0.521845 0.853041i \(-0.674756\pi\)
−0.521845 + 0.853041i \(0.674756\pi\)
\(464\) 2.14575 + 3.71655i 0.0996140 + 0.172537i
\(465\) −19.2915 + 33.4139i −0.894622 + 1.54953i
\(466\) 8.46863 14.6681i 0.392302 0.679486i
\(467\) −5.35425 9.27383i −0.247765 0.429142i 0.715140 0.698981i \(-0.246363\pi\)
−0.962905 + 0.269839i \(0.913029\pi\)
\(468\) 20.0000 0.924500
\(469\) −10.4170 −0.481012
\(470\) −48.4575 −2.23518
\(471\) −28.0000 48.4974i −1.29017 2.23464i
\(472\) −0.322876 + 0.559237i −0.0148616 + 0.0257410i
\(473\) 2.00000 3.46410i 0.0919601 0.159280i
\(474\) −3.50000 6.06218i −0.160760 0.278445i
\(475\) −2.93725 −0.134770
\(476\) 7.93725 13.7477i 0.363803 0.630126i
\(477\) −14.5830 −0.667710
\(478\) 4.61438 + 7.99234i 0.211057 + 0.365561i
\(479\) 12.9686 22.4623i 0.592552 1.02633i −0.401336 0.915931i \(-0.631454\pi\)
0.993887 0.110399i \(-0.0352127\pi\)
\(480\) −4.82288 + 8.35347i −0.220133 + 0.381282i
\(481\) 4.11438 + 7.12631i 0.187600 + 0.324932i
\(482\) −22.8118 −1.03905
\(483\) 12.7601 + 22.1012i 0.580606 + 1.00564i
\(484\) 1.00000 0.0454545
\(485\) 10.4059 + 18.0235i 0.472507 + 0.818406i
\(486\) 10.5830 18.3303i 0.480055 0.831479i
\(487\) 15.2915 26.4857i 0.692924 1.20018i −0.277951 0.960595i \(-0.589655\pi\)
0.970875 0.239585i \(-0.0770113\pi\)
\(488\) 1.85425 + 3.21165i 0.0839379 + 0.145385i
\(489\) 12.2915 0.555841
\(490\) 12.7601 + 22.1012i 0.576444 + 0.998430i
\(491\) 10.7085 0.483268 0.241634 0.970367i \(-0.422317\pi\)
0.241634 + 0.970367i \(0.422317\pi\)
\(492\) −6.53137 11.3127i −0.294457 0.510015i
\(493\) 12.8745 22.2993i 0.579839 1.00431i
\(494\) −0.885622 + 1.53394i −0.0398460 + 0.0690153i
\(495\) −7.29150 12.6293i −0.327729 0.567643i
\(496\) −4.00000 −0.179605
\(497\) 12.7601 + 22.1012i 0.572370 + 0.991374i
\(498\) 35.1660 1.57583
\(499\) −8.93725 15.4798i −0.400086 0.692970i 0.593650 0.804724i \(-0.297687\pi\)
−0.993736 + 0.111754i \(0.964353\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 20.1458 34.8935i 0.900046 1.55893i
\(502\) 3.64575 + 6.31463i 0.162718 + 0.281836i
\(503\) −19.9373 −0.888958 −0.444479 0.895789i \(-0.646611\pi\)
−0.444479 + 0.895789i \(0.646611\pi\)
\(504\) −5.29150 + 9.16515i −0.235702 + 0.408248i
\(505\) 10.9373 0.486701
\(506\) −1.82288 3.15731i −0.0810367 0.140360i
\(507\) 15.8745 27.4955i 0.705012 1.22112i
\(508\) −0.0313730 + 0.0543397i −0.00139195 + 0.00241093i
\(509\) −10.2915 17.8254i −0.456163 0.790097i 0.542591 0.839997i \(-0.317443\pi\)
−0.998754 + 0.0498996i \(0.984110\pi\)
\(510\) 57.8745 2.56273
\(511\) −14.9373 −0.660785
\(512\) −1.00000 −0.0441942
\(513\) −0.468627 0.811686i −0.0206904 0.0358368i
\(514\) −0.208497 + 0.361128i −0.00919643 + 0.0159287i
\(515\) −23.5830 + 40.8470i −1.03919 + 1.79993i
\(516\) −5.29150 9.16515i −0.232945 0.403473i
\(517\) 13.2915 0.584560
\(518\) −4.35425 −0.191315
\(519\) −27.2288 −1.19521
\(520\) 9.11438 + 15.7866i 0.399692 + 0.692287i
\(521\) 1.06275 1.84073i 0.0465598 0.0806439i −0.841806 0.539780i \(-0.818508\pi\)
0.888366 + 0.459136i \(0.151841\pi\)
\(522\) −8.58301 + 14.8662i −0.375668 + 0.650676i
\(523\) −7.76013 13.4409i −0.339327 0.587731i 0.644979 0.764200i \(-0.276866\pi\)
−0.984306 + 0.176469i \(0.943533\pi\)
\(524\) 15.6458 0.683488
\(525\) −29.0203 + 50.2646i −1.26655 + 2.19373i
\(526\) −4.06275 −0.177144
\(527\) 12.0000 + 20.7846i 0.522728 + 0.905392i
\(528\) 1.32288 2.29129i 0.0575708 0.0997155i
\(529\) 4.85425 8.40781i 0.211054 0.365557i
\(530\) −6.64575 11.5108i −0.288673 0.499996i
\(531\) −2.58301 −0.112093
\(532\) −0.468627 0.811686i −0.0203176 0.0351910i
\(533\) −24.6863 −1.06928
\(534\) 19.2915 + 33.4139i 0.834825 + 1.44596i
\(535\) −9.00000 + 15.5885i −0.389104 + 0.673948i
\(536\) 1.96863 3.40976i 0.0850317 0.147279i
\(537\) −5.37451 9.30892i −0.231927 0.401710i
\(538\) −26.5830 −1.14607
\(539\) −3.50000 6.06218i −0.150756 0.261116i
\(540\) −9.64575 −0.415087
\(541\) 4.14575 + 7.18065i 0.178240 + 0.308720i 0.941278 0.337633i \(-0.109626\pi\)
−0.763038 + 0.646354i \(0.776293\pi\)
\(542\) −8.96863 + 15.5341i −0.385236 + 0.667247i
\(543\) −13.2288 + 22.9129i −0.567700 + 0.983286i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) 38.5830 1.65271
\(546\) 17.5000 + 30.3109i 0.748931 + 1.29719i
\(547\) 27.5203 1.17668 0.588341 0.808613i \(-0.299781\pi\)
0.588341 + 0.808613i \(0.299781\pi\)
\(548\) −9.43725 16.3458i −0.403140 0.698258i
\(549\) −7.41699 + 12.8466i −0.316550 + 0.548280i
\(550\) 4.14575 7.18065i 0.176775 0.306184i
\(551\) −0.760130 1.31658i −0.0323826 0.0560883i
\(552\) −9.64575 −0.410550
\(553\) 3.50000 6.06218i 0.148835 0.257790i
\(554\) 11.7085 0.497446
\(555\) −7.93725 13.7477i −0.336918 0.583559i
\(556\) 2.00000 3.46410i 0.0848189 0.146911i
\(557\) −15.8745 + 27.4955i −0.672624 + 1.16502i 0.304533 + 0.952502i \(0.401500\pi\)
−0.977157 + 0.212518i \(0.931834\pi\)
\(558\) −8.00000 13.8564i −0.338667 0.586588i
\(559\) −20.0000 −0.845910
\(560\) −9.64575 −0.407607
\(561\) −15.8745 −0.670222
\(562\) −3.53137 6.11652i −0.148962 0.258010i
\(563\) −6.53137 + 11.3127i −0.275265 + 0.476772i −0.970202 0.242298i \(-0.922099\pi\)
0.694937 + 0.719070i \(0.255432\pi\)
\(564\) 17.5830 30.4547i 0.740378 1.28237i
\(565\) 14.0516 + 24.3381i 0.591157 + 1.02391i
\(566\) 7.64575 0.321375
\(567\) 13.2288 0.555556
\(568\) −9.64575 −0.404727
\(569\) 20.5830 + 35.6508i 0.862884 + 1.49456i 0.869133 + 0.494579i \(0.164678\pi\)
−0.00624806 + 0.999980i \(0.501989\pi\)
\(570\) 1.70850 2.95920i 0.0715611 0.123947i
\(571\) 22.4686 38.9168i 0.940283 1.62862i 0.175351 0.984506i \(-0.443894\pi\)
0.764932 0.644112i \(-0.222773\pi\)
\(572\) −2.50000 4.33013i −0.104530 0.181052i
\(573\) 35.1660 1.46908
\(574\) 6.53137 11.3127i 0.272614 0.472182i
\(575\) −30.2288 −1.26063
\(576\) −2.00000 3.46410i −0.0833333 0.144338i
\(577\) 12.7288 22.0469i 0.529905 0.917823i −0.469486 0.882940i \(-0.655561\pi\)
0.999391 0.0348828i \(-0.0111058\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) −15.2399 26.3962i −0.633347 1.09699i
\(580\) −15.6458 −0.649654
\(581\) 17.5830 + 30.4547i 0.729466 + 1.26347i
\(582\) −15.1033 −0.626050
\(583\) 1.82288 + 3.15731i 0.0754958 + 0.130763i
\(584\) 2.82288 4.88936i 0.116811 0.202323i
\(585\) −36.4575 + 63.1463i −1.50733 + 2.61078i
\(586\) 6.00000 + 10.3923i 0.247858 + 0.429302i
\(587\) −7.93725 −0.327606 −0.163803 0.986493i \(-0.552376\pi\)
−0.163803 + 0.986493i \(0.552376\pi\)
\(588\) −18.5203 −0.763763
\(589\) 1.41699 0.0583863
\(590\) −1.17712 2.03884i −0.0484614 0.0839377i
\(591\) 24.9686 43.2469i 1.02707 1.77894i
\(592\) 0.822876 1.42526i 0.0338200 0.0585779i
\(593\) −11.4686 19.8642i −0.470960 0.815727i 0.528488 0.848941i \(-0.322759\pi\)
−0.999448 + 0.0332139i \(0.989426\pi\)
\(594\) 2.64575 0.108556
\(595\) 28.9373 + 50.1208i 1.18631 + 2.05475i
\(596\) −4.70850 −0.192868
\(597\) −29.4059 50.9325i −1.20350 2.08453i
\(598\) −9.11438 + 15.7866i −0.372715 + 0.645561i
\(599\) 9.87451 17.1031i 0.403461 0.698816i −0.590680 0.806906i \(-0.701140\pi\)
0.994141 + 0.108090i \(0.0344736\pi\)
\(600\) −10.9686 18.9982i −0.447792 0.775599i
\(601\) −24.5830 −1.00276 −0.501381 0.865227i \(-0.667174\pi\)
−0.501381 + 0.865227i \(0.667174\pi\)
\(602\) 5.29150 9.16515i 0.215666 0.373544i
\(603\) 15.7490 0.641350
\(604\) 1.67712 + 2.90486i 0.0682412 + 0.118197i
\(605\) −1.82288 + 3.15731i −0.0741104 + 0.128363i
\(606\) −3.96863 + 6.87386i −0.161214 + 0.279232i
\(607\) −10.6458 18.4390i −0.432098 0.748415i 0.564956 0.825121i \(-0.308893\pi\)
−0.997054 + 0.0767058i \(0.975560\pi\)
\(608\) 0.354249 0.0143667
\(609\) −30.0405 −1.21730
\(610\) −13.5203 −0.547419
\(611\) −33.2288 57.5539i −1.34429 2.32838i
\(612\) −12.0000 + 20.7846i −0.485071 + 0.840168i
\(613\) −1.00000 + 1.73205i −0.0403896 + 0.0699569i −0.885514 0.464614i \(-0.846193\pi\)
0.845124 + 0.534570i \(0.179527\pi\)
\(614\) −2.11438 3.66221i −0.0853294 0.147795i
\(615\) 47.6235 1.92037
\(616\) 2.64575 0.106600
\(617\) −16.2915 −0.655871 −0.327936 0.944700i \(-0.606353\pi\)
−0.327936 + 0.944700i \(0.606353\pi\)
\(618\) −17.1144 29.6430i −0.688441 1.19242i
\(619\) −17.2915 + 29.9498i −0.695004 + 1.20378i 0.275175 + 0.961394i \(0.411264\pi\)
−0.970179 + 0.242388i \(0.922069\pi\)
\(620\) 7.29150 12.6293i 0.292834 0.507203i
\(621\) −4.82288 8.35347i −0.193535 0.335213i
\(622\) −16.9373 −0.679122
\(623\) −19.2915 + 33.4139i −0.772898 + 1.33870i
\(624\) −13.2288 −0.529574
\(625\) −1.14575 1.98450i −0.0458301 0.0793800i
\(626\) 1.20850 2.09318i 0.0483013 0.0836603i
\(627\) −0.468627 + 0.811686i −0.0187152 + 0.0324156i
\(628\) 10.5830 + 18.3303i 0.422308 + 0.731459i
\(629\) −9.87451 −0.393722
\(630\) −19.2915 33.4139i −0.768592 1.33124i
\(631\) 34.8118 1.38583 0.692917 0.721017i \(-0.256325\pi\)
0.692917 + 0.721017i \(0.256325\pi\)
\(632\) 1.32288 + 2.29129i 0.0526212 + 0.0911425i
\(633\) −19.7601 + 34.2255i −0.785395 + 1.36034i
\(634\) 6.00000 10.3923i 0.238290 0.412731i
\(635\) −0.114378 0.198109i −0.00453896 0.00786172i
\(636\) 9.64575 0.382479
\(637\) −17.5000 + 30.3109i −0.693375 + 1.20096i
\(638\) 4.29150 0.169902
\(639\) −19.2915 33.4139i −0.763160 1.32183i
\(640\) 1.82288 3.15731i 0.0720555 0.124804i
\(641\) 9.43725 16.3458i 0.372749 0.645620i −0.617238 0.786776i \(-0.711749\pi\)
0.989987 + 0.141156i \(0.0450819\pi\)
\(642\) −6.53137 11.3127i −0.257773 0.446475i
\(643\) 6.52026 0.257134 0.128567 0.991701i \(-0.458962\pi\)
0.128567 + 0.991701i \(0.458962\pi\)
\(644\) −4.82288 8.35347i −0.190048 0.329173i
\(645\) 38.5830 1.51920
\(646\) −1.06275 1.84073i −0.0418132 0.0724226i
\(647\) −19.4059 + 33.6120i −0.762924 + 1.32142i 0.178413 + 0.983956i \(0.442904\pi\)
−0.941337 + 0.337467i \(0.890430\pi\)
\(648\) −2.50000 + 4.33013i −0.0982093 + 0.170103i
\(649\) 0.322876 + 0.559237i 0.0126740 + 0.0219520i
\(650\) −41.4575 −1.62610
\(651\) 14.0000 24.2487i 0.548703 0.950382i
\(652\) −4.64575 −0.181942
\(653\) −1.17712 2.03884i −0.0460644 0.0797859i 0.842074 0.539362i \(-0.181335\pi\)
−0.888138 + 0.459576i \(0.848001\pi\)
\(654\) −14.0000 + 24.2487i −0.547443 + 0.948200i
\(655\) −28.5203 + 49.3985i −1.11438 + 1.93016i
\(656\) 2.46863 + 4.27579i 0.0963837 + 0.166941i
\(657\) 22.5830 0.881047
\(658\) 35.1660 1.37091
\(659\) 14.5830 0.568073 0.284037 0.958813i \(-0.408326\pi\)
0.284037 + 0.958813i \(0.408326\pi\)
\(660\) 4.82288 + 8.35347i 0.187730 + 0.325158i
\(661\) −14.2915 + 24.7536i −0.555875 + 0.962804i 0.441960 + 0.897035i \(0.354283\pi\)
−0.997835 + 0.0657690i \(0.979050\pi\)
\(662\) −7.67712 + 13.2972i −0.298380 + 0.516809i
\(663\) 39.6863 + 68.7386i 1.54129 + 2.66959i
\(664\) −13.2915 −0.515810
\(665\) 3.41699 0.132505
\(666\) 6.58301 0.255086
\(667\) −7.82288 13.5496i −0.302903 0.524643i
\(668\) −7.61438 + 13.1885i −0.294609 + 0.510278i
\(669\) −16.3431 + 28.3071i −0.631862 + 1.09442i
\(670\) 7.17712 + 12.4311i 0.277277 + 0.480257i
\(671\) 3.70850 0.143165
\(672\) 3.50000 6.06218i 0.135015 0.233854i
\(673\) −14.9373 −0.575789 −0.287894 0.957662i \(-0.592955\pi\)
−0.287894 + 0.957662i \(0.592955\pi\)
\(674\) 12.4686 + 21.5963i 0.480274 + 0.831858i
\(675\) 10.9686 18.9982i 0.422183 0.731242i
\(676\) −6.00000 + 10.3923i −0.230769 + 0.399704i
\(677\) 1.06275 + 1.84073i 0.0408446 + 0.0707450i 0.885725 0.464210i \(-0.153662\pi\)
−0.844880 + 0.534955i \(0.820328\pi\)
\(678\) −20.3948 −0.783256
\(679\) −7.55163 13.0798i −0.289805 0.501957i
\(680\) −21.8745 −0.838849
\(681\) −17.5830 30.4547i −0.673782 1.16703i
\(682\) −2.00000 + 3.46410i −0.0765840 + 0.132647i
\(683\) 6.96863 12.0700i 0.266647 0.461846i −0.701347 0.712820i \(-0.747418\pi\)
0.967994 + 0.250974i \(0.0807509\pi\)
\(684\) 0.708497 + 1.22715i 0.0270901 + 0.0469214i
\(685\) 68.8118 2.62916
\(686\) −9.26013 16.0390i −0.353553 0.612372i
\(687\) 42.3320 1.61507
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) 9.11438 15.7866i 0.347230 0.601420i
\(690\) 17.5830 30.4547i 0.669374 1.15939i
\(691\) 9.38562 + 16.2564i 0.357046 + 0.618422i 0.987466 0.157833i \(-0.0504506\pi\)
−0.630420 + 0.776254i \(0.717117\pi\)
\(692\) 10.2915 0.391224
\(693\) 5.29150 + 9.16515i 0.201008 + 0.348155i
\(694\) −26.8118 −1.01776
\(695\) 7.29150 + 12.6293i 0.276582 + 0.479055i
\(696\) 5.67712 9.83307i 0.215191 0.372721i
\(697\) 14.8118 25.6547i 0.561035 0.971742i
\(698\) 14.9373 + 25.8721i 0.565383 + 0.979273i
\(699\) −44.8118 −1.69494
\(700\) 10.9686 18.9982i 0.414575 0.718065i
\(701\) −6.87451 −0.259647 −0.129823 0.991537i \(-0.541441\pi\)
−0.129823 + 0.991537i \(0.541441\pi\)
\(702\) −6.61438 11.4564i −0.249644 0.432395i
\(703\) −0.291503 + 0.504897i −0.0109942 + 0.0190426i
\(704\) −0.500000 + 0.866025i −0.0188445 + 0.0326396i
\(705\) 64.1033 + 111.030i 2.41427 + 4.18164i
\(706\) 35.1660 1.32349
\(707\) −7.93725 −0.298511
\(708\) 1.70850 0.0642093
\(709\) 3.40588 + 5.89916i 0.127911 + 0.221548i 0.922867 0.385119i \(-0.125840\pi\)
−0.794956 + 0.606667i \(0.792506\pi\)
\(710\) 17.5830 30.4547i 0.659878 1.14294i
\(711\) −5.29150 + 9.16515i −0.198447 + 0.343720i
\(712\) −7.29150 12.6293i −0.273261 0.473301i
\(713\) 14.5830 0.546138
\(714\) −42.0000 −1.57181
\(715\) 18.2288 0.681717
\(716\) 2.03137 + 3.51844i 0.0759160 + 0.131490i
\(717\) 12.2085 21.1457i 0.455935 0.789702i
\(718\) −5.03137 + 8.71459i −0.187769 + 0.325226i
\(719\) 1.93725 + 3.35542i 0.0722474 + 0.125136i 0.899886 0.436125i \(-0.143650\pi\)
−0.827639 + 0.561261i \(0.810316\pi\)
\(720\) 14.5830 0.543477
\(721\) 17.1144 29.6430i 0.637373 1.10396i
\(722\) 18.8745 0.702436
\(723\) 30.1771 + 52.2683i 1.12230 + 1.94388i
\(724\) 5.00000 8.66025i 0.185824 0.321856i
\(725\) 17.7915 30.8158i 0.660760 1.14447i
\(726\) −1.32288 2.29129i −0.0490965 0.0850377i
\(727\) −17.2915 −0.641306 −0.320653 0.947197i \(-0.603902\pi\)
−0.320653 + 0.947197i \(0.603902\pi\)
\(728\) −6.61438 11.4564i −0.245145 0.424604i
\(729\) −41.0000 −1.51852
\(730\) 10.2915 + 17.8254i 0.380906 + 0.659748i
\(731\) 12.0000 20.7846i 0.443836 0.768747i
\(732\) 4.90588 8.49723i 0.181327 0.314067i
\(733\) −20.7288 35.9033i −0.765634 1.32612i −0.939911 0.341420i \(-0.889092\pi\)
0.174277 0.984697i \(-0.444241\pi\)
\(734\) 9.77124 0.360663
\(735\) 33.7601 58.4743i 1.24526 2.15686i
\(736\) 3.64575 0.134384
\(737\) −1.96863 3.40976i −0.0725153 0.125600i
\(738\) −9.87451 + 17.1031i −0.363486 + 0.629576i
\(739\) 3.93725 6.81952i 0.144834 0.250860i −0.784477 0.620158i \(-0.787068\pi\)
0.929311 + 0.369298i \(0.120402\pi\)
\(740\) 3.00000 + 5.19615i 0.110282 + 0.191014i
\(741\) 4.68627 0.172154
\(742\) 4.82288 + 8.35347i 0.177053 + 0.306665i
\(743\) −34.7085 −1.27333 −0.636666 0.771140i \(-0.719687\pi\)
−0.636666 + 0.771140i \(0.719687\pi\)
\(744\) 5.29150 + 9.16515i 0.193996 + 0.336011i
\(745\) 8.58301 14.8662i 0.314457 0.544655i
\(746\) −5.43725 + 9.41760i −0.199072 + 0.344803i
\(747\) −26.5830 46.0431i −0.972621 1.68463i
\(748\) 6.00000 0.219382
\(749\) 6.53137 11.3127i 0.238651 0.413356i
\(750\) 31.7490 1.15931
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) −6.64575 + 11.5108i −0.242346 + 0.419755i
\(753\) 9.64575 16.7069i 0.351511 0.608834i
\(754\) −10.7288 18.5828i −0.390718 0.676744i
\(755\) −12.2288 −0.445050
\(756\) 7.00000 0.254588
\(757\) 19.1660 0.696600 0.348300 0.937383i \(-0.386759\pi\)
0.348300 + 0.937383i \(0.386759\pi\)
\(758\) 10.9686 + 18.9982i 0.398398 + 0.690046i
\(759\) −4.82288 + 8.35347i −0.175059 + 0.303212i
\(760\) −0.645751 + 1.11847i −0.0234239 + 0.0405713i
\(761\) 3.00000 + 5.19615i 0.108750 + 0.188360i 0.915264 0.402854i \(-0.131982\pi\)
−0.806514 + 0.591215i \(0.798649\pi\)
\(762\) 0.166010 0.00601393
\(763\) −28.0000 −1.01367
\(764\) −13.2915 −0.480870
\(765\) −43.7490 75.7755i −1.58175 2.73967i
\(766\) −17.0516 + 29.5343i −0.616101 + 1.06712i
\(767\) 1.61438 2.79619i 0.0582918 0.100964i
\(768\) 1.32288 + 2.29129i 0.0477352 + 0.0826797i
\(769\) −15.1660 −0.546900 −0.273450 0.961886i \(-0.588165\pi\)
−0.273450 + 0.961886i \(0.588165\pi\)
\(770\) −4.82288 + 8.35347i −0.173804 + 0.301038i
\(771\) 1.10326 0.0397331
\(772\) 5.76013 + 9.97684i 0.207312 + 0.359074i
\(773\) −1.29150 + 2.23695i −0.0464521 + 0.0804574i −0.888317 0.459232i \(-0.848125\pi\)
0.841864 + 0.539689i \(0.181458\pi\)
\(774\) −8.00000 + 13.8564i −0.287554 + 0.498058i
\(775\) 16.5830 + 28.7226i 0.595679 + 1.03175i